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Thread: complex variables, determining shape?

  1. #1
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    complex variables, determining shape?

    The question is to sketch the set of points determined by the equation.
    |3z - 2i|>= 4

    I know that if it was say |z -1 - 2i| = 2 that its a circle centered at (1,2) with radius 2. But im not sure how to interpret the above equation.
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  2. #2
    Super Member craig's Avatar
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    Try dividing by 3, should help you along
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    okay so now I have that |z-2/3 i|>=4/3 so im interpretting this as center of the circle is at 2/3i and radius is 4/3 and since the inequality is >= i want everything outside of the circle. Does this make sense?
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  4. #4
    Super Member craig's Avatar
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    Quote Originally Posted by scubasteve123 View Post
    okay so now I have that |z-2/3 i|>=4/3 so im interpretting this as center of the circle is at 2/3i and radius is 4/3 and since the inequality is >= i want everything outside of the circle. Does this make sense?
    Yep that seems right from here.

    Just remember that as the inequality is $\displaystyle \geq$, you will need to include the line of the circle as well.
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